# A college professor believes that students take an average of 15

A college professor   believes that students take an average of 15 credit hours per semester. A   random sample of 24 students in his class of 250 reported the following   number of credit hours that they were taking:   12,13,14,14,15,15,15,16,16,16,16,16,17,17,17,18,18,18,18,19,19,19,20,21    Does this sample indicate that   students are taking more credit hours than the professor believes? BEFORE   jumping to an answer, work through this problem using the following steps:   1) What are your null and alternative   hypotheses? Answer verbally and with mathematical symbols.   2) One condition to check is that the   data should be “Nearly normal”, or roughly unimodal and symmetric. Create a   histogram or box plot of the data and assess this condition.   3) Is the sampling distribution of the   mean a z or a student’s t statistic? Why?   4) Specify the decision rule using a = .05.   5) Sketch a normal curve graphic   identifying the critical value and rejection area labeling the mean and the   values. It is OK to draw this by hand and scan it into your document.   6) Calculate the test statistic using   MegaStat.   7) Make the decision and state your   conclusion in the context of this problem.   8) Regardless of its statistical   significance, comment on the practical importance of the difference in credit   load.   9) If this sample of students was   extremely unusual and your conclusion was wrong (based on the entire   population of students taking this professor’s classes), what type error   would you be committing? Why?   10) Find a 95% confidence interval for   the number of credit hours taken by the students in the professor’s class.   Summarize what this interval means in one or two sentences.

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